Chapter 3

Mobile Radio Propagation

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Outline

• Types of Waves• Radio Frequency Bands• Propagation Mechanisms• Free-Space Propagation• Land Propagation• Path Loss• Fading: Slow Fading / Fast Fading• Doppler Shift/Delay Spread• Intersymbol Interference• Coherence Bandwidth/Co-Channel Interference

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Speed, Wavelength, Frequency

System Frequency Wavelength

AC current 60 Hz 5,000 km

FM radio 100 MHz 3 m

Cellular 800 MHz 37.5 cm

Ka band satellite 20 GHz 15 mm

Ultraviolet light 1015 Hz 10-7 m

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Light speed = Wavelength x Frequency

= 3 x 108 m/s = 300,000 km/s

Types of Waves

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Transmitter Receiver

Earth

Sky wave

Space wave

Ground waveTroposphere

(0 - 12 km)

Stratosphere (12 - 50 km)

Mesosphere (50 - 80 km)

Ionosphere (80 - 720 km)

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Band Name Frequency Wavelength Applications

Extremely low frequency (ELF)

30 to 300 Hz 10000 to 1000 Km Powerline frequencies

Voice Frequency (VF) 300 to 3000 Hz 1000 to 100 Km Telephone communications

Very low frequency (VLF)

3 to 30 KHz 100 to 10 Km Marine communications

Low frequency (LF) 30 to 300 KHz 10 to 1 Km Marine communications

Medium frequency (MF)

300 to 3000 KHz 100 to 100 m AM broadcasting

High frequency (HF) 3 to 30 MHz 100 to 10 m Long-distance aircraft / ship communications

Very high frequency (VHF)

30 to 300 MHz 10 to 1 m FM broadcasting

Ultra high frequency (UHF)

300 to 3000 MHz 100 to 10 cm Cellular telephone

Super high frequency (SHF)

3 to 30 GHz 10 to 1 cm Satellite communications, microwave links

Extremely high frequency (EHF)

30 to 300 GHZ 10 to 1 mm Wireless local loop

Infrared 300 GHz to 400 THz 1 mm to 400 nm Consumer electronics

Visible light 400 THz to 900 THz 770 nm to 330 um Optical communications

Frequency bands and their common uses

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Radio Frequency Bands

Classification Band Initials Frequency Range Characteristics

Extremely low ELF < 300 Hz

Ground waveInfra low ILF 300 Hz - 3 kHz

Very low VLF 3 kHz - 30 kHz

Low LF 30 kHz - 300 kHz

Medium MF 300 kHz - 3 MHz Ground/Sky wave

High HF 3 MHz - 30 MHz Sky wave

Very high VHF 30 MHz - 300 MHz

Space waveUltra high UHF 300 MHz - 3 GHz

Super high SHF 3 GHz - 30 GHz

Extremely high EHF 30 GHz - 300 GHz

Tremendously high THF 300 GHz - 3000 GHz

Propagation Mechanisms

• Reflection– Propagation wave impinges on an object which is large as

compared to wavelength, e.g., the surface of the Earth, buildings, walls, etc.

• Diffraction– Radio path between transmitter and receiver obstructed by

surface with sharp irregular edges

– Waves bend around the obstacle, even when LOS (line of sight) does not exist

• Scattering– Objects smaller than the wavelength of the propagation

wave

- e.g. foliage, street signs, lamp posts

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Reflected Signal

Scattered Signal

Receiver

Direct Signal

Diffracted Signal

Transmitter

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Radio Propagation Effects

Free-space Propagation

• The received signal power Pr at distance d:

where Pt is transmitting power, Ae is effective area of an antenna, and Gt

is the transmitting antenna gain. Assuming that the radiated power is

uniformly distributed over the surface of the sphere.9

Transmitter Distance dReceiver

hb

hm

,4 2d

PGAP

tter

rG

,4

2 e

rA

G 2)/4( d

PGGP

ttrr

Antenna Gain

• Relationship between antenna gain and effective area:Gain G = 4 Ae / 2 = 4 f 2Ae /c2, = carrier wavelength,

f = carrier frequency, and c = speed of light

• Example:Antenna with Ae = 0.55 , frequency = 6 GHz,

wavelength = 0.05 m → G = 39.4 dBFrequency = 14 GHz, same diameter, wavelength =

0.021 m → G = 46.9 dB Higher the frequency, higher the gain for the same size

antenna10

Decibel- dB

• Decibel is the unit used to express relative differences in signal strength

• It is expressed as the base 10 logarithm of the ratio of the powers of two signals:– dB = 10 log (P1/P2)

• Logarithms are useful as the unit of measurement – signal power tends to span several orders of

magnitude

– signal attenuation losses and gains can be expressed in terms of subtraction and addition

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12

• Suppose that a signal passes through two channels is first attenuated in the ratio of 20 and 7 on the second. The total signal degradation is the ratio of 140 to 1. Expressed in dB, this become 10 log 20 + 10 log 7 = 13.01 + 8.45 = 21.46 dB

Example

The Order of dB

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The following table helps to indicate the order of magnitude associated with dB:– 1 dB attenuation means that 0.79 of the input power

survives.– 3 dB attenuation means that 0.5 of the input power

survives.– 10 dB attenuation means that 0.1 of the input power

survives.– 20 dB attenuation means that 0.01 of the input power

survives.– 30 dB attenuation means that 0.001 of the input power

survives.– 40 dB attenuation means that 0.0001 of the input power

survives.

Land Propagation

• The received signal power:

where L is the propagation loss in the channel, i.e.,

L = LP LS LF

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L

PGGP trt

r

Fast fading

Slow fading

Path loss

Path Loss (Free-space)

The path loss LP is the average propagation loss over a wide area.

Slow fading is long-term fading and fast fading is short-term fading.

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Path Loss: The signal strength decays exponentially with distance d between transmitter and receiver;

The loss could be proportional to somewhere between d2 and d4 depending on the environment.

r

tP P

PL

Path Loss (Land Propagation)

Simplest Formula:

Lp = A dα

where

A and α: propagation constants

d : distance between transmitter and receiver

α : value of 3 ~ 4 in typical urban area

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Example of Path Loss (Free-space)

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Path Loss in Free-space

70

80

90

100

110

120

130

0 5 10 15 20 25 30

Distance d (km)

Path

Los

s Lf

(dB)

fc=150MHz

fc=200MHz

fc=400MHz

fc=800MHz

fc=1000MHz

fc=1500MHz

Path Loss

• Path loss in decreasing order:– Urban area (large city)

– Urban area (medium and small city)

– Suburban area

– Open area

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Fading

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Signal Strength

(dB)

Distance

Path Loss

Slow Fading (Long-term fading)

Fast Fading (Short-term fading)

Slow Fading

• Slow fading is caused by the long-term spatial and temporal variations over distances large enough to produce gross variations in the overall path between transmitter and receiver.

• The long-term variation in the mean level is known as slow fading. Slow fading is also called shadowing or log-normal fading.

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Shadowing

• Shadowing: Often there are millions of tiny

obstructions in the channel, such as water droplets if

it is raining or the individual leaves of trees. Because

it is too cumbersome to take into account all the

obstructions in the channel, these effects are typically

lumped together into a random power loss.

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Fast Fading

• The signal from the transmitter may be reflected from objects such as hills, buildings, or vehicles. Fast fading is due to scattering of the signal by object near transmitter.

• Fast fading (short-term fading) Observe the distance of about half a wavelength Such as multipath propagation

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Doppler Shift (1/2)

Doppler Effect: When a wave source and a receiver are moving towards each other, the frequency of the received signal will not be the same as the source.When they are moving toward each other, the frequency of

the received signal is higher than the source.When they are opposing each other, the frequency

decreases.Thus, the frequency of the received signal is

where fC is the frequency of source carrier, fD is the Doppler frequency.

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DCR fff

Doppler Shift (2/2)

• Doppler Shift in frequency:

where v is the moving speed, is the wavelength of carrier.

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MS

Signal

Moving speed v

cosv

fD

Moving Speed Effect

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Time

V1 V2 V3 V4

Sig

nal

str

engt

h

Delay Spread

• When a signal propagates from a transmitter to a receiver, signal suffers one or more reflections.

• This forces signal to follow different paths.

• Each path has different path length, so the time of arrival for each path is different.

• This effect which spreads out the signal is called “Delay Spread”.

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Delay Spread

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Delay

Sig

nal

Str

engt

hThe signals from close by reflectors

The signals from intermediate reflectors

The signals from far away reflectors

Inter-Symbol Interference (ISI)

• Caused by time delayed multipath signals• Has impact on burst error rate of channel• Second multipath is delayed and is received

during next symbol

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Inter-Symbol Interference (ISI)

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Time

Time

Time

Transmission signal

Received signal (short delay)

Received signal (long delay)

1

0

1

Propagation timeDelayed signals

Homework

• Problems: 3.2, 3.4, 3.12, 3.14 (Due: Oct. 4)

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